Wireless power transfer to biomedical implants

ABSTRACT

Various examples are provided for wireless power transfer to implants. In one example, a system includes a radio frequency (RF) power source and a transmitter (TX) array comprising an excitation coil and resonant coils distributed about the excitation coil. The TX array can transfer power from the RF power source to a biomedical implant inserted below a skin surface of a subject when the TX array is positioned on the skin surface adjacent to the biomedical implant. A receiver (RX) coil of the biomedical implant can inductively couple with the TX array for the power transfer. The resonant coils can allow power transfer when the RX coil is not aligned with the excitation coil.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation that claims priority to, and thebenefit of, co-pending U.S. non-provisional application having Ser. No.16/644,863, filed Mar. 5, 2020, which is a national stage entry pursuantto 35 U.S.C. § 371 of International Application No. PCT/US2018/049526,filed on Sep. 5, 2018, which claims the benefit of and priority to U.S.provisional Application entitled “Wireless Power Transfer to BiomedicalImplants” having Ser. No. 62/554,251, filed Sep. 5, 2017, all of whichare hereby incorporated by reference in their entireties.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with government support under DE-AC52-06NA25396awarded by the Department of Energy. The Government has certain rightsin this invention.

BACKGROUND

The continuous trend towards low power integrated circuit design hasresulted in microsystems for body area networks, RFID transponders, andbiomedical implants operating at sub-milliwatt power levels. One designchallenge for biomedical implants is the ability to supply sufficientpower while maintaining a small form factor. For larger scale systems,battery power is a natural solution. For microsystems, battery power isless attractive due to low energy generation density per unit area. As aresult, achieving the small form factor needed for biomedical implantsor other microsystems can be difficult to achieve.

SUMMARY

Aspects of the present disclosure are related to wireless power transferto implants. In one aspect, among others, a system for wireless powertransfer to biomedical implants comprises a radio frequency (RF) powersource; and a transmitter (TX) array comprising an excitation coil and aplurality of resonant coils distributed about the excitation coil. TheTX array can be configured to transfer power from the RF power source toa biomedical implant inserted below a skin surface of a subject when theTX array is positioned on the skin surface adjacent to the biomedicalimplant. In one or more aspects, each resonant coil of the plurality ofresonant coils can be adjacent to the excitation coil and two otherresonant coils of the plurality of resonant coils. The excitation coiland individual resonant coils of the plurality of resonant coils canhave a substantially square shape. The area of the excitation coil canbe approximately 4 times the area of each resonant coil of the pluralityof resonant coils. For example, the excitation coil can surrounded by 12resonant coils.

In various aspects, the excitation coil and the plurality of resonantcoils can be formed on a printed circuit board (PCB). The PCB can beconfigured to affix to the skin surface. The excitation coil and theplurality of resonant coils can be multi-turn coils disposed on bothsides of the PCB. The excitation coil and the plurality of resonantcoils can comprise two spirally-wound turns on each side of the PCB. Inone or more aspects, the RF power source can excite the excitation coilvia an RF power amplifier. The biomedical implant can comprise areceiver (RX) coil that inductively couples with the TX array for thepower transfer. The RX coil can be an on-chip RX coil. The RX coil canbe approximately equal in size to each of the plurality of resonantcoils or can be smaller than the resonant coils. The TX array cantransfer power to the RX coil with a misalignment factor (MF) of up to150%, where the MF is the lateral separation of a center of the RX coilfrom a center of the excitation coil normalized to a size of each of theplurality of resonant coils.

In one or more aspects, the plurality of resonant coils can comprises afirst layer of resonant coils located adjacent to the excitation coil,and a second layer of resonant coils located outside the first layer ofresonant coils opposite the excitation coil. Individual resonant coilsof the first layer or the second layer can be separated from adjacentresonant coils in that layer by a uniform distance. The TX array can beconfigured to transfer power to the biomedical implant when a receiver(RX) coil extends beyond the second layer of resonant coils, and is notlocated below the first layer of resonant coils. In various aspects, thesystem can comprise a flexible substrate, where the TX array is formedon the flexible substrate with the plurality of resonant coilssymmetrically surrounding the excitation coil. The plurality of resonantcoils can comprise a plurality of concentric layers of resonant coilssurrounding the excitation coil.

Other systems, methods, features, and advantages of the presentdisclosure will be or become apparent to one with skill in the art uponexamination of the following drawings and detailed description. It isintended that all such additional systems, methods, features, andadvantages be included within this description, be within the scope ofthe present disclosure, and be protected by the accompanying claims. Inaddition, all optional and preferred features and modifications of thedescribed embodiments are usable in all aspects of the disclosure taughtherein. Furthermore, the individual features of the dependent claims, aswell as all optional and preferred features and modifications of thedescribed embodiments are combinable and interchangeable with oneanother.

BRIEF DESCRIPTION OF THE DRAWINGS

Many aspects of the present disclosure can be better understood withreference to the following drawings. The components in the drawings arenot necessarily to scale, emphasis instead being placed upon clearlyillustrating the principles of the present disclosure. Moreover, in thedrawings, like reference numerals designate corresponding partsthroughout the several views.

FIG. 1 is an image illustrating an example of a wireless power transfer(WPT) platform for minimally invasive or shallow biomedical implants, inaccordance with various embodiments of the present disclosure.

FIGS. 2A and 2B are graphical representations of examples of WPTtopologies comprising a transmitter (TX) coil and TX array respectively,in accordance with various embodiments of the present disclosure.

FIG. 3 is a schematic diagram illustrating an example of a WPT systemcomprising a TX array, in accordance with various embodiments of thepresent disclosure.

FIG. 4A is a die micrograph of an example of an on-chip receiver (RX),in accordance with various embodiments of the present disclosure.

FIGS. 4B-4D are plots illustrating simulated and measured data forquality factor, input resistance, and input reactance of an on-chip RXcoil of FIG. 4A, in accordance with various embodiments of the presentdisclosure.

FIG. 5 is a plot illustrating simulated and measured data for qualityfactor of an excitation coil of a TX array, in accordance with variousembodiments of the present disclosure.

FIG. 6A illustrates an example of a transmitter (TX) array comprising anexcitation coil and resonant coils, in accordance with variousembodiments of the present disclosure.

FIG. 6B includes schematic diagrams illustrating examples of amisalignment factor (MF) between a TX array (or excitation coil) and areceiver coil, in accordance with various embodiments of the presentdisclosure.

FIG. 7 illustrates a simplified cross-section of an average human armwith a table indicating frequency dependent tissue dielectric propertiesper layer, in accordance with various embodiments of the presentdisclosure.

FIG. 8 is a flow diagram illustrating an example of the determination ofan optimal load impedance and power transfer efficiency (PTE), inaccordance with various embodiments of the present disclosure.

FIGS. 9A and 9B graphically illustrate examples of electromagneticsimulation results for magnetic field intensity and surface currentdensity of a TX array of FIG. 6A, respectively, in accordance withvarious embodiments of the present disclosure.

FIG. 10 illustrates the construction and properties of an example of acompound tissue equivalent phantom, in accordance with variousembodiments of the present disclosure.

FIG. 11 illustrates an example of an experimental test setup forevaluation of WPT systems, in accordance with various embodiments of thepresent disclosure.

FIG. 12 is a plot illustrating measured PTE with respect to MF for a TXarray topology and an equivalent loop, in accordance with variousembodiments of the present disclosure.

FIG. 13 is a table illustrating a comparison of WPT systems, inaccordance with various embodiments of the present disclosure.

DETAILED DESCRIPTION

Disclosed herein are various examples related to wireless power transferto biomedical implants such as, e.g., near-field wireless power transferto on-chip receiver coils using a transmitter array topology. In orderto achieve a small form factor for biomedical implants or othermicrosystems, wireless power transfer (WPT) techniques can be utilized.However, conventional WPT systems are limited by the degradation ofpower transfer efficiency due to misalignment between the transmitterand receiver coils. While WPT offers the additional advantage ofuntethered operation, orientation and location of a biomedical implantmay not be precisely known. This problem is further compounded by thesmall implant size.

In addition, in vivo WPT occurs through tissue with distinct dielectricproperties leading to higher losses, and lower power transferefficiency, in contrast to conventional WPT through air. Severalfrequency bands such as, e.g., ISM 13.56 MHz, MedRadio 401-406 MHz andISM 902-928 MHz have been considered for WPT to biomedical implants. Thechoice of the transmission frequency is a trade-off between the powerrequirement, human body impact, implant size, transmission medium, andtransmission distance. At frequencies below 1 MHz, large implant sizesare needed to obtain sufficient power. At microwave frequencies, thebody absorbs electromagnetic energy, increasing transmission loss. Anoptimum frequency can be determined that maximizes efficiency whilekeeping energy density below the specific absorption rate (SAR) toprevent tissue damage. As always, patient comfort and safety areimportant considerations in the design of biomedical implants.

Reference will now be made in detail to the description of theembodiments as illustrated in the drawings, wherein like referencenumbers indicate like parts throughout the several views. A transmitterarray topology is disclosed for wireless power transfer to lateral or 2Dmisaligned implants. In this topology, a single excitation coilresonantly couples energy throughout the array. The power transferefficiency can be enhanced by optimizing the transmitter-receivercoupling coefficient, and the power transfer ratio between the arrayelements. To demonstrate the performance of the disclosed array topologyunder different misalignment factors, a transmitter array with an areaof 852.6 mm² was fabricated on an FR4 substrate. The transmitter arraysupplied power to a 4 mm×4 mm subcutaneous implant with an on-chipreceiver fabricated in 90-nm CMOS technology. A variation in powertransfer efficiency of less than 2.6 dB was obtained with 150%misalignment factor in both horizontal and vertical directions.

Referring to FIG. 1 , shown is an example of a WPT platform forminimally invasive or shallow biomedical implants that can be used fordiagnostic and therapeutic purposes such as, e.g., glucose monitoring. Akey attraction of these implant types is the ability to continuouslymonitor biological processes not readily accessible outside the body. Anexternal transmitter, worn as a flexible skin patch, wirelessly powersthe implant via inductive coupling between the transmitter and animplanted coil. As illustrated in FIG. 1 , the biomedical implant isinserted just beneath the patch using an implant insert instrument.Biomedical implants with wireless power capability have the potential toeliminate secondary battery replacement surgeries lasting on averagebetween one to three hours, and hospitalization of several days.

In controlled inductive WPT systems, it is desirable that transmitterand receiver coils are aligned to maximize the mutual coupling and powertransfer efficiency (PTE). In practical implementations transmitter andreceiver coils may not be aligned. Therefore, development of advancedWPT techniques to improve transmitter-receiver coupling and PTE betweenmisaligned coils is beneficial. A conventional WPT approach for poweringan implant with a single transmitter (TX) coil 203 through the tissue206 is illustrated in FIG. 2A. The conventional method uses a largertransmitter (TX) coil 203 to supply power to an implant via a smallerreceiver (RX) coil 209 to reduce the effect of misalignment. Thisresults in a large amount of leakage flux that does not couple with thesmaller RX coil 209.

FIG. 2B illustrates an example of a TX array 212 that can be used tosupply power to the implant via the RX coil 209. The disclosed topologyuses an array of resonant transmitter elements to enhance thetransmitter-receiver coupling coefficient. An overview of the WPT systemwith the RX coil 209 and TX array 212 separated by a transmission medium(e.g., tissue) 206, and its performance, will be presented. A procedureto determine optimum load for maximum power transfer efficiency, in aWPT system with an arbitrary RX coil 209 and TX array 212 will also bediscussed. In addition, simulation and experimental results of theimplemented WPT system in tissue equivalent phantoms designed to mimicbiological media are presented.

As illustrated in FIG. 2B, a transmitter array topology is proposed toimprove efficiency and mitigate performance degradation due to lateraltransmitter-receiver misalignment. The TX array 212 can be fabricated onan FR4 board, while the RX coil 209 can be an on-chip coil fabricated in90-nm CMOS technology. As shown in FIG. 2A, conventional WPT uses asingle large transmitter coil 203 leading to a low PTE due to poortransmitter-receiver flux linkage, while the transmitter topology withthe TX array 212 of FIG. 2B uses elements of similar size leading tostronger near-field coupling between transmitter array 212 and receivercoil 209.

Referring to FIG. 3 , shown is a schematic diagram illustrating anexample of the WPT system. A series-parallel compensation topology canbe utilized for voltage amplification at low power levels. For powertransmission, an RF power amplifier 303 with low output resistance canbe used to drive the TX array 212 from a RF source 306. In the implant,a rectifier 309 and filter capacitor 312 provide RF to DC conversion ofpower received by the on-chip RX coil 209 to supply an arbitrary sensorload 315. A tissue equivalent phantom was embedded between the TX array212 and RX coil 209 to emulate WPT through a biological media 206.

In a single transmitter and receiver WPT system, the maximum powertransfer efficiency can be estimated by:

${\eta_{\max} = \frac{k^{2}Q_{t}Q_{r}}{( {1 + {k^{2}Q_{t}Q_{r}}} )}},$

where k is the coupling coefficient, Q_(t) is the loaded quality factorof the TX coil 203, and Q_(r) is the loaded quality factor of theon-chip RX coil 209. System performance is therefore heavily dependenton transmitter quality factor, receiver quality factor, andtransmitter-receiver coupling coefficient which in turn depends on thetransmission medium 206.

On-Chip Receiver Coil. A die micrograph of the on-chip receiver (RX) isshown in FIG. 4A. The on-chip receiver coil 209 was fabricated in 90-nmCMOS technology with an overall size of 4 mm×4 mm. For simplicity, asingle layer 4-tum on-chip coil 209 was fabricated with a trackthickness of 3.25 μm, track width of 25 μm, and track spacing of 35 μm.The topmost metal layer, metal 9, was used to minimize sheet resistance.A large core area was reserved for energy storage, power management,sensor readout, and data telemetry.

Measured and simulated data of quality factor, input resistance, andinput reactance of the on-chip RX coil are shown in FIGS. 4B, 4C and 4D,respectively. The on-chip RX coil 209 had a self-resonant frequency(SRF) of 235 MHz, effectively restricting the operating frequency tobelow 200 MHz for a quality factor greater than unity. On-chip coilshave lower quality factors and self-resonant frequencies than theiroff-chip counterparts due to thinner metal layers, high turn density,and layer-to-substrate parasitic capacitance. The quality factor is alsodegraded due to the tissue dielectric environment. Despite their lowquality factors, miniaturization of implantable coils using integratedcircuit technologies yields a compact millimeter scale design attractivefor biomedical implants and other microsystems.

Transmitter Array. Referring now to FIG. 6A, shown is an example of atransmitter (TX) array 212, which comprises an excitation coil 603 andresonant coils 606. FIG. 6A shows the layout of the fabricated TX array212 on an FR4 printed circuit board (PCB) substrate. The excitation coil603 is located at the center of the TX array 212, while the resonantcoils 606 are surrounding elements. An input or excitation signal isprovided to the excitation coil 603, and the resonant coils 606 coupleelectromagnetic energy throughout the TX array 212.

In the example of FIG. 6A, the TX array 212 comprises 12 resonant coils606 surrounding the excitation coil 603. The TX array 212 canequivalently be described as having an overall size of 4×4 resonantelements 606, with a center excitation coil 603 equivalent in size tofour resonant elements 606. The coils 603 and 606 have a square shape,which allows the resonant coils 606 to be tightly distributed in asymmetrical configuration about the excitation coil 603. For example,the resonant elements or coils 606 can each have a size of 6.7 mm×6.7 mmand the excitation element or coil 603 can have a size of 13.4 mm×13.4mm, yielding a total TX array size of 29.2 mm×29.2 mm. Other geometriccoil shapes (e.g., rectangular, hexagonal, octagonal, etc.) may also beutilized. While a single layer of resonant coils 606 is shownsurrounding the excitation coil 603, multiple layers of resonant coils606 may be provided in other implementations.

Measured and simulated data for the quality factor of the excitationelement 603 is shown in FIG. 5 . The inset table provides transmitterspecifications of track width, spacing, and thickness for the excitationcoil 606. Quality factor was computed from the measured coil resistanceand reactance values. Measured resistance was on the order of 0.5Ω,which was a bit low for proper resolution by a network analyzer. Tocharacterize the PTE between the transmitter array and a receiver coil,a misalignment factor (MF) is introduced to quantify position variation.The MF is defined as the lateral separation of the RX coil 209 from thetransmitter center (center of TX array 212 or excitation coil 603)normalized to the resonant element size. FIG. 6B includes schematicdiagrams illustrating four examples of different transmitter-receiverhorizontal MFs.

The misalignment factor (MF) can be expressed as a percentage, and canbe specified in one or more directions (e.g., horizontal and/orvertical). Various transmitter-receiver horizontal MFs are illustratedin FIG. 6B. The larger square with the solid line represents the outerdimensions of the excitation element 603, the square with the dashedline represents a portion of excitation element 603 with an equivalentsize as the RX coil 209, and the smaller square with the solid linerepresents the outer dimensions of the RX coil 209 position. The TXarray topology provides field coverage of up to 150% MF in bothhorizontal and vertical directions as illustrated in FIG. 6B. The upperleft diagram illustrates 0% MF with the excitation coil 603 aligned withthe RX coil 209. The upper right diagram illustrates 50% MF with the RXcoil 209 offset from the transmitter center and aligned with one edge ofthe excitation coil 603. The lower left diagram illustrates 100% MF withthe excitation coil 603 overlapping half of the RX coil 209. In thiscase, a portion of the resonant coils 606 overlaps the other half of theRX coil 209. The lower right diagram illustrates 150% MF with the RXcoil 209 misaligned with the excitation coil 603 and adjacent to one ormore resonant coils 606. Additional field coverage is possible usingmore resonant elements 606 with an added penalty of lower power transferefficiencies. The choice of transmitter size can depend on theanticipated misalignment tolerance, and a desired power transferefficiency.

Tissue Equivalent Phantom. The implemented WPT system comprising the TXarray 212 of FIG. 6B was evaluated using tissue equivalent phantoms toemulate wireless power transfer to a subcutaneous implant insertedunderneath the skin of an individual. Design of tissue equivalentphantoms at frequencies ranging from 30 MHz to 300 MHz was needed due tothe significant difference in dielectric properties between live andposthumous tissue just 1 hour after death. A simplified cross-section ofan average human arm is shown in FIG. 7 . This simplified abstractioncomprises four layers, namely skin, fat, muscle and bone. The table atthe bottom of FIG. 7 indicates the thickness and frequency dependenttissue dielectric properties specified per layer.

As can be understood, an important objective in tissue equivalentphantom design is to create phantoms with dielectric properties thatapproximate actual tissue for a desired frequency range. In the exampleof FIG. 7 , the target conductivity and relative permittivity for eachtissue layer is specified at 40.68 MHz, 89 MHz, and 125 MHz. Thesephantom design points were chosen to evaluate performance of theimplemented WPT system. As seen in FIG. 4B, the RX coil 209 has anoptimum unloaded quality factor in air of 3 at 110 MHz. This qualityfactor will be degraded by the dielectric loading of the tissueequivalent phantom.

Design and Optimization. The transmitter operates on the principle ofresonant magnetic coupling. The magnetic field originating from theexcitation coil 603 couples throughout the transmitter array 212 and tothe receiver. From Kirchhoffs circuit laws, a system of linear equationsdescribing energy distribution for an inductively coupled WPT system canbe written as:

$\begin{matrix}{{ZI} = {V = {{\begin{bmatrix}Z_{11} & Z_{12} & Z_{13} & Z_{14} \\Z_{21} & Z_{22} & Z_{23} & Z_{24} \\Z_{31} & Z_{32} & Z_{33} & Z_{34} \\Z_{41} & Z_{42} & Z_{43} & Z_{44}\end{bmatrix}\begin{bmatrix}I_{1} \\I_{2} \\I_{3} \\I_{4}\end{bmatrix}} = {\begin{bmatrix}V_{1} \\0 \\0 \\0\end{bmatrix}.}}}} & (1)\end{matrix}$

Z denotes the impedance matrix, I denotes the current phasor vector, andV denotes the voltage phasor vector. V₁ corresponds to the excitationcoil voltage and I₁ corresponds to the excitation coil current.Self-impedance of each coil, Z_(ii)=R_(i)+jωL_(i)−1/jωC_(i) is afunction of self-inductance, parasitic resistance, and resonantcapacitance. Mutual-impedance between coils, Z_(ij)=jωk√{square rootover (L_(i)L_(j))}=jωM_(ij) for i≠j, is a function of self-inductancesand coupling coefficient.

A modified impedance matrix {circumflex over (Z)} is obtained afterdeleting row one from the impedance matrix Z as shown in:

$\begin{matrix}{{\overset{\hat{}}{Z}I} = {{\begin{bmatrix}Z_{21} & Z_{22} & Z_{23} & Z_{24} \\Z_{31} & Z_{32} & Z_{33} & Z_{34} \\Z_{41} & Z_{42} & Z_{43} & Z_{44}\end{bmatrix}\begin{bmatrix}1 \\{I_{2}/I_{1}} \\{I_{3}/I_{1}} \\{I_{4}/I_{1}}\end{bmatrix}} = 0.}} & (2)\end{matrix}$

The null space of {circumflex over (Z)}, N({circumflex over (Z)}),expressed as a vector of current transfer ratios with respect toexcitation current is a solution to the matrix equation. For a WPTsystem with N transmitter array elements and one receiver coil,{circumflex over (Z)} has N by N+1 dimensions since its matrix isaugmented by an additional row and column due to mutual impedancesbetween the receiver and transmitter array elements. The currenttransfer ratio (CTR) can then be given by 1, I₂/I₁, I₃/I₁, . . . ,I_(N)/I₁. Total power consumption is the sum of power delivered to theload, power dissipated by the transmitter, and power dissipated by thereceiver. The power transfer efficiency can be specified as:

$\begin{matrix}{{\eta = \frac{{❘I_{LOAD}❘}^{2} \cdot R_{LOAD}}{\lbrack {\sum_{i = 1}^{N + 1}{{❘I_{i}❘}^{2} \cdot R_{i}}} \rbrack + {{❘I_{LOAD}❘}^{2} \cdot R_{LOAD}}}},} & (3)\end{matrix}$

which is consistent with PTE derivation by K. Lee et al in “Analysis ofWireless Power Transfer for Adjustable Power Distribution among MultipleReceivers” (IEEE Antennas Wirel. Propag. Lett., vol. 14, pp. 950-953,2015). PTE can be rewritten as:

$\begin{matrix}{{\eta = \frac{R_{LOAD}}{\lbrack {{❘\frac{I_{1}}{I_{LOAD}}❘}^{2}{\sum_{i = 1}^{N + 1}{{❘\frac{I_{i}}{I_{1}}❘}^{2} \cdot R_{i}}}} \rbrack + R_{LOAD}}},} & (4)\end{matrix}$

which a function of CTR squared or power transfer ratio betweentransmitter coils, parasitic resistance, and load resistance.

A series equivalent load impedance, Z_(OPT)=R_(LOAD-OPT)+jX_(LOAD-OPT),has been derived for maximum power transmission efficiency in a singletransmitter-receiver topology. This optimum impedance can be restatedas:

$\begin{matrix}{{R_{{LOAD} - {OPT}} = \frac{\sqrt{( {{rZ_{11}rZ_{22}} + {iZ_{12}^{2}}} )( {{rZ_{11}rZ_{22}} - {rZ_{12}^{2}}} )}}{rZ_{11}}},} & (5)\end{matrix}$ $\begin{matrix}{{X_{{LOAD} - {OPT}} = {\frac{iZ_{12}rZ_{12}}{rZ_{11}} - {iZ}_{22}}},} & (6)\end{matrix}$

with the real and imaginary parts of Z-parameters prefixed by r and i,respectively. The optimum load impedance range can be derived from:

$\begin{matrix}{R_{{LOAD} - {OPT}} = \frac{ \sqrt{( {A + B} )( {A - C} } )}{rZ_{11}}} & (7)\end{matrix}$ $\begin{matrix}{A = {rZ_{11}rZ_{{N + 1},{N + 1}}}} & {B = {iZ_{1,{N + 1}}^{2}}} & {C = {rZ_{1,{N + 1}}^{2}}}\end{matrix}$ $\begin{matrix}{{rZ}_{{N + 1},{N + 1}} < R_{{LOAD} - {OPT}} < \frac{A\sqrt{1 + \frac{B}{A}}}{rZ_{11}}} & (8)\end{matrix}$$B = ( {\omega k_{1,{N + 1}}\sqrt{L_{1}L_{N + 1}}} )^{2}$$\begin{matrix}{C = ( {k_{1,{N + 1}}\sqrt{\frac{L_{N + 1}}{L_{1}}}rZ_{{N + 1},{N + 1}}} )^{2}} & (9)\end{matrix}$ $\begin{matrix}{{k_{\max} = {{\max( k_{1,{N + 1}} )} \geq k_{1,{N + 1}}}},\ {1 \leq i \leq N}} & (10)\end{matrix}$ $\begin{matrix}{{rZ}_{{N + 1},{N + 1}} < R_{{LOAD} - {OPT}} < {rZ_{{N + 1},{N + 1}}\sqrt{1 + \frac{( {\omega k_{\max}\sqrt{L_{1}L_{N + 1}}} )^{2}}{rZ_{11}rZ_{{N + 1},{N + 1}}}}}} & (11)\end{matrix}$ $\begin{matrix}{{{{- i}Z_{{N + 1},{N + 1}}} < X_{{LOAD} - {OPT}} < {\frac{\sqrt{BC}}{rZ_{11}} - {iZ_{{N + 1},{N + 1}}}}},} & (12)\end{matrix}$ $\begin{matrix}{{{{- i}Z_{{N + 1},{N + 1}}} < X_{{LOAD} - {OPT}} < {\frac{\omega k_{\max}^{2}L_{N + 1}rZ_{{N + 1},{N + 1}}}{rZ_{11}} - {iZ_{{N + 1},{N + 1}}}}},} & (13)\end{matrix}$

A bounded scanning algorithm, executable by a computing device or otherprocessing circuitry, can be implemented to calculate the optimum loadin a multi transmitter-receiver topology from equations (7) through(13). In equation (11), the optimum load resistance R_(LOAD-OPT) isbounded by the parasitic resistance of the receiver coil. The impedancerange is a function of receiver self-inductance, receiver parasiticresistance, transmitter self-inductance, transmitter parasiticresistance, and maximum coupling coefficient. A series-parallelconversion can be applied to obtain component values consistent with theWPT system of FIG. 3 .

FIG. 8 shows a flow chart illustrating an example of the determinationof the optimum load, which can prove useful since a closed formexpression for a transmitter array topology with many elements iscomplex. Beginning at 803, the load resistance, load reactance andoptimal power transfer efficiency (PTE_(OPT)) are initialized. The loadreactance is incremented (e.g., by a defined value) at 806 and the coilself-impedances are determined at 809. The null space of the modifiedimpedance matrix of equation (2) is determined at 812 and the PTE isdetermined at 815 using equation (4), which is compared to PTE_(OPT) at818. If the PTE is greater than the PTE_(OPT), then the optimal powertransfer efficiency and optimal load reactance are set to the powertransfer efficiency and load reactance at 821 before comparing the loadreactance to a maximum reactance value at 824. If the PTE is not greaterat 818, then the flow proceeds to 824 for the comparison. If the loadreactance is less than the maximum reactance value, then the flowreturns to 806 where the load reactance is again incremented.

If the load reactance is greater or equal to the maximum reactancevalue, then the load resistance is incremented (e.g., by a definedvalue) at 827 and the coil self-impedances are determined at 830 usingthe optimal load reactance. The null space of the modified impedancematrix of equation (2) is again determined at 833 and the PTE isdetermined at 836 using equation (4), which is compared to PTE_(OPT) at839. If the PTE is greater than the PTE_(OPT), then the optimal powertransfer efficiency and optimal load resistance are set to the powertransfer efficiency and load resistance at 842 before comparing the loadresistance to a maximum resistance value at 845. If the PTE is notgreater at 839, then the flow proceeds to 845 for the comparison. If theload resistance is less than the maximum resistance value, then the flowreturns to 827 where the load resistance is again incremented. If theload reactance is greater or equal to the maximum reactance value, thenthe optimal load impedance is defined using the optimal load resistanceand the optimal load reactance at 848. As can be understood by thosereasonably skilled in the art of the present disclosure, alternateimplementations are included within the scope of the present disclosurein which descriptions or blocks in flow chart may be executed out oforder from that shown or discussed, including substantially concurrentlyor in reverse order, depending on the functionality involved.

Simulation and Measurement Results. Full-wave electromagneticsimulations were performed using ANSYS HFSS to obtain the impedancematrix {circumflex over (Z)} as a function of operation frequency,transmission distance, and lateral misalignment. The reactive componentof self-impedance for each array element 603 and 606 (FIG. 6A) was thenused to compute its resonant capacitance. The impedance matrix wasimported into MATLAB and the scanning algorithm procedure illustrated inFIG. 8 was implemented to determine the optimum load impedance and powertransfer efficiency. The above procedure was performed for eachoperation frequency, transmission distance, and lateral misalignment tocharacterize the WPT system.

Results of the full-wave electromagnetic simulations showing magneticfield intensity and surface current density of the transmitter array andthe on-chip receiver coil are shown in FIGS. 9A and 9B. The magneticfield intensity is plotted in FIG. 9A and the surface current density isplotted in FIG. 9B. The electromagnetic field distribution or surfacecurrent density of the TX array 212 is shown on the left. Through themechanism of resonant inductive coupling, electromagnetic energy iscoupled from the excitation element 603, throughout the array structure.

The electromagnetic field distribution (and current density) of the RXcoil 209 when positioned 10 mm underneath the excitation coil 603 at thecenter of TX array 212 is shown at the center of FIGS. 9A and 9B. Thisalignment has a 0% MF, or perfect alignment, which is consistent withFIG. 6B. The field distribution (and current density) of the RX coil 209when positioned between the excitation coil 603 and resonant coil 606 aof the TX array 212 is shown on the right of FIGS. 9A and 9B. Thisalignment has a 100% horizontal and vertical MF.

Tissue equivalent phantoms were designed to mimic dielectric propertiesof biological media. Referring to FIG. 10 , shown is an image of anexample of a compound tissue equivalent phantom comprising skin and fatphantom layers. Phantom development was restricted to skin and fatlayers since the biomedical application space is subcutaneous implantsat a depth of about 10 mm from the skin's surface. Individual phantomlayers were formed by pouring phantom gels into 30 printed fixtures madefrom ABS plastic. The skin and fat fixtures have thicknesses of 1.5 mmand 8.5 mm, respectively. Once these layered phantom gels solidify, acompound phantom was formed is illustrated in FIG. 10 .

A hydrous based phantom was designed for the skin layer, and an oilbased phantom was designed for the fat layer. Table I of FIG. 10 liststhe percent weight proportions for skin and fat tissue equivalentphantoms. The hydrous skin phantom consists of deionized (DI) water,sucrose, TX-151 powder, and sodium chloride. Sucrose can be used tocontrol relative permittivity, sodium chloride can be used to controlconductivity, and TX-151 can be used to control gelation. The oil basedfat phantom consists of oil, flour, deionized water, and sodiumhydroxide. Sodium hydroxide can be used as a surfactant, while oil andflour can both be used to control permittivity.

Measured phantom dielectric properties at 40.68 MHz, 89 MHz, and 125 MHzare shown in Table II of FIG. 10 . The phantom dielectric propertieswere determined from measured scattering parameters and the conductivitywas calculated using the Debye relation (“Agilent Basics of Measuringthe Dielectric Properties of Materials,” Agilent, pp. 1-31). Themeasured conductivity and relative permittivity are a reasonableapproximation of the target tissue dielectric properties of FIG. 7 .

An experimental test setup for the wireless power transmission system isshown in FIG. 11 . An RF signal source 1103 drives the TX array 212shown in the upper right view through two terminal connections of theexcitation coil 603. An enlarged view of the compound tissue equivalentphantom and its enclosing fixture is shown in the middle right view. Thecompound phantom was positioned between the TX array 212 and the on-chipRX coil 209 to mimic the biological media. The on-chip RX coil 209 inthe bottom right view was packaged as a chip-on-board 1106 with an SMAconnector for measuring the receiver signal level. An expanded view ofthe receiver die micrograph was shown in FIG. 4A.

An equivalent loop with an area of 852.6 mm², a track width of 1.5 mm, atrack spacing of 3 mm, a track thickness of 35 μm, and 2 turns per layeron an FR4 substrate was designed as a comparison baseline for the TXarray 212. Performance of the equivalent loop and TX array 212 wasdetermined at 0% MF which corresponds to perfect alignment, 50% MF, 100%MF, and 150% MF in both horizontal and/or vertical directions.

Measured power transfer efficiency with optimum load conditions for theWPT system with the transmitter 1103, tissue equivalent phantom media,and chip-on-board 1106 with the RX coil 209 using the measurement setupof FIG. 11 . FIG. 12 shows the measurement results of the PTE at atransmitter-receiver distance of 10 mm the different MFs. The solidcurve 1203 shows the measured PTE of the transmitter array topology foronly horizontal MF, the dashed curve 1206 shows the measured PTE of thetransmitter array with equal horizontal and vertical MF, the solid curve1209 shows PTE of the equivalent loop for only horizontal MF and thedashed curve 1212 shows PTE with equal horizontal and vertical MF as acomparison baseline. For the transmitter array topology, a maximumefficiency of −24.9 dB or 0.32% was achieved at 0% MF. For 50%horizontal and/or vertical MF, PTE remained virtual unchanged. At 150%MF in both horizontal and vertical directions, a worst case PTE of −27.4dB or 0.18% was obtained. The variation in PTE was 2.52 dB between bestand worst case alignments for the transmitter array topology. For theequivalent loop, a maximum efficiency of −28.1 dB or 0.16% was achievedat 0% MF. At 150% MF in both horizontal and vertical directions, a PTEof −42.1 dB or 0.006% was obtained. The variation in PTE was 14 dBbetween best and worst case alignments for the equivalent loop. Thetransmitter array offers a PTE improvement of 3.1 dB at 0% MF and 14.7dB at 150% MF in both horizontal and vertical directions.

Referring now to FIG. 13 , shown is a comparison of WPT systems tobiomedical implants. Various WPT systems for shallow biomedical implantsare shown in Table III of FIG. 13 . Design choices of transmitter size,operation frequency, implant size, and implant technology differ acrossvarious implementations. Because it is desirable to minimize implantsize while maintaining high power transfer efficiency, a figure of merit(FOM=η(%). A_(TX)/A_(RX)) has been introduced to quantify performance;where η is the power transfer efficiency, A_(TX) is the area of theexternal transmitter, and A_(RX) is the area of the implanted receiver.

For a one-to-one WPT system, the transmitter and receiver coils haveequal areas, which results in a high coupling coefficient when both areperfectly aligned. One-to-one implementations are not practical forsmall biomedical implants since perfect alignment to an externaltransmitter is not feasible. As a result, none of the reportedimplementations in Table III of FIG. 13 use this method. TheA_(TX)/A_(RX) term in the FOM therefore accounts for the misalignmenttolerance.

For a best case scenario in which the receiver coil is aligned at thecenter of a transmitter coil, power transfer efficiency is maximized.However, misalignment data is not reported. In this disclosure, designfor misalignment was implemented using a transmitter array structure (TXarray 212) with an excitation element 603 and resonant elements 606approximately equal in area to the RX coil 209. Performance of the WPTsystem is reported for various misalignment factors as shown in TableIII of FIG. 13 .

The external transmitter coils are typically implemented on PCB, whileimplantable receiver coils have been designed on PCB, as wire woundcoils or micro-fabricated coils. PCB coils are cheapest to design andfabricate, but cannot be easily miniaturized to achieve a small implantsize. Wire wound coils have the highest quality factor performance, andcan be miniaturized using painstakingly wound turns. However,fabrication and integration costs are high. A micro-fabricated on-chipcoil in 90-nm CMOS technology was used for this evaluation. On-chipcoils have the lowest quality factor performance, but offer lowintegration cost and can easily be miniaturized. In spite of their lowquality factor, careful design procedures can be used to optimize systemperformance.

A WPT platform with misalignment tolerance was implemented herein, witha basic single layer on-chip receiver coil designed with noco-optimization of transmitter and receiver coils. The measured qualityfactor of the basic on-chip receiver coil was less than 3 between 50 MHzand 160 MHz. In “Fully Integrated On-Chip Coil in 0.13 CMOS for WirelessPower Transfer through Biological Media” by M. Zargham et al. (IEEETrans. Biomed. Circuits Syst., vol 9, no. 2, pp. 259-271, 2015), a duallayer on-chip coil was implemented and transmitter-receiver coils wereco-designed for optimum power transfer efficiency. As a result, areceiver coil quality factor greater than 8 was obtained between 50 MHzand 160 MHz.

The operating frequency can vary across WPT system implementations. Forexample, “Design and Optimization of a 3-coil Inductive Link forEfficient Wireless Power Transmission” by M. Kiani et al. (IEEE Trans.Biomed Circuits Syst., vol. 5, no. 6. pp. 519-591, 2011) used the 13.56MHz ISM band, “Resonant Inductive Link for Remote Powering ofPacemakers” by G. Monti et al. (IEEE Trans. Microw. Theory Techn., vol.63, no 11, pp. 3814-3822, 2015) used 403 MHz MedRadio band, and “Amm-Sized Implantable Power Receiver with Adoptive Link Compensation” byS. O'Driscoll et al. (IEEE Solid-State Circuits Conf. Dig. Tech. Papers,pp. 294-295, 2009) used the 915 MHz ISM band. The design choice ofoperation frequency is a tradeoff between receiver technology, receiversize, and system performance. Operating at high frequencies appearsattractive due to its potential to reduce implant coil size. A WPTsystem operating at 1600 MHz was been implemented in “Wireless PowerTransfer to Deep-Tissue Micro-Implants” by J. S. Ho et al. (Proc. Natl.Acad. Sci. U.S.A. vol. 111, no. 22, pp. 7974-7979, 2014), resulting in asmall receiver coil size of 3.14 mm². Operation at such high frequenciesis possible due to high self-resonant frequencies of wire wound coils.However, at high frequencies significant absorption of electromagneticenergy occurs in the tissue media. The system operating at 1600 MHz hasa very low efficiency of 0.04% as shown in Table III of FIG. 13 . Thesystem operating at 13.56 MHz exhibited the highest efficiency of 6.9%for a PCB receiver coil. However, its implant coil area of 78 mm² islarge. For micro-fabricated CMOS coils disclosed herein and in “FullyIntegrated On-Chip Coil in 0.13 CMOS for Wireless Power Transfer throughBiological Media” by M. Zargham et al., the self-resonant frequency islow due to high tum-to-tum and layer-to-substrate parasitic capacitance.A self-resonant frequency of 235 MHz in this work sets an upper bound onthe operation frequency. An operation frequency of 89 MHz was used foroptimum power transfer efficiency between the TX array 212 and a 4 mm×4mm receiver on-chip coil.

In summary, a maximum FOM of 68.8 was obtained in “Wireless PowerTransfer to Deep-Tissue Micro-Implants” by Ho et al. However, its customwire wound receiver uses expensive fabrication, integration, andpackaging processes. In “Design and Optimization of a 3-coil InductiveLink for Efficient Wireless Power Transmission” by M. Kiani et al.,“Resonant Inductive Link for Remote Powering of Pacemakers” by G. Montiet al., and “A mm-Sized Implantable Power Receiver with Adoptive LinkCompensation” by S. O'Driscoll et al., the receiver coils werefabricated on a PCB which tended to be large and increase implant size.“Fully Integrated On-Chip Coil in 0.13 CMOS for Wireless Power Transferthrough Biological Media” by M. Zargham et al. implemented amicrofabricated coil and reports the second highest FOM due to its duallayer receiver and co-design of transmitter-receiver coils. However,none of these WPT systems account for misalignment tolerance. In thisdisclosure, design for misalignment tolerance was incorporated on thetransmitter side. However, the fabricated on-chip receiver was notoptimized for maximum quality factor. A significant improvement inquality factor is possible using multi-layers with optimized trackwidth, spacing, and number of turns. The disclosed design procedure canoptimize power transfer efficiency for a WPT system with an arbitrarynon-optimal receiver.

A novel transmitter array topology has been presented for WPT to amisaligned transmitter-receiver system. Tissue equivalent phantomscomprising skin and fat layers were developed to demonstrate wirelesspower transmission to shallow biomedical implants. A scanning algorithmto compute an optimum load impedance was disclosed for a transmitterarray topology, in order to simplify design of a WPT system withmultiple elements. Performance of the WPT system was demonstrated usinga 4 mm×4 mm micro-fabricated implantable receiver coil in 90-nm CMOStechnology and an external PCB transmitter array coil.

A FOM based on the implant size, power transfer efficiency, and degreeof misalignment was introduced to evaluate the system performance.Despite using a non-optimal micro-fabricated receiver coil with a lowquality factor, a maximum FOM of 17 was reported as shown in Table IIIof FIG. 13 . At 150% MF in both horizontal and vertical directions, theFOM was 9.6 which exceeds the performance of a perfectly aligned WPTsystem reported in “Resonant Inductive Link for Remote Powering ofPacemakers” by G. Monti et al. and “A mm-Sized Implantable PowerReceiver with Adoptive Link Compensation” by S. O'Driscoll et al. Thedesign methodology and techniques in this disclosure can be applied totackle misalignment problems often encountered in WPT systems.

It should be emphasized that the above-described embodiments of thepresent disclosure are merely possible examples of implementations setforth for a clear understanding of the principles of the disclosure.Many variations and modifications may be made to the above-describedembodiment(s) without departing substantially from the spirit andprinciples of the disclosure. All such modifications and variations areintended to be included herein within the scope of this disclosure andprotected by the following claims.

The term “substantially” is meant to permit deviations from thedescriptive term that don't negatively impact the intended purpose.Descriptive terms are implicitly understood to be modified by the wordsubstantially, even if the term is not explicitly modified by the wordsubstantially.

It should be noted that ratios, concentrations, amounts, and othernumerical data may be expressed herein in a range format. It is to beunderstood that such a range format is used for convenience and brevity,and thus, should be interpreted in a flexible manner to include not onlythe numerical values explicitly recited as the limits of the range, butalso to include all the individual numerical values or sub-rangesencompassed within that range as if each numerical value and sub-rangeis explicitly recited. To illustrate, a concentration range of “about0.1% to about 5%” should be interpreted to include not only theexplicitly recited concentration of about 0.1 wt % to about 5 wt %, butalso include individual concentrations (e.g., 1%, 2%, 3%, and 4%) andthe sub-ranges (e.g., 0.5%, 1.1%, 2.2%, 3.3%, and 4.4%) within theindicated range. The term “about” can include traditional roundingaccording to significant figures of numerical values. In addition, thephrase “about ‘x’ to ‘y’” includes “about ‘x’ to about ‘y’”.

Therefore, at least the following is claimed:
 1. A method for wirelesspower transfer, comprising: positioning a transmitter (TX) arrayadjacent to a receiver (RX) coil of a device, the TX array comprising anexcitation coil excited by a radio frequency (RF) power source and alayer of passive, non-overlapping resonant coils distributed about andsurrounding the excitation coil, where each resonant coil of the layerof passive, non-overlapping resonant coils is adjacent to the excitationcoil and two other resonant coils of the layer of passive,non-overlapping resonant coils; and transferring power from the RF powersource to the RX coil by coupling a magnetic field originating from theexcitation coil throughout the TX array thereby allowing coupling withthe RX coil when overlapping at least a portion of the layer of passive,non-overlapping resonant coils without overlapping the excitation coil.2. The method of claim 1, wherein the RX coil is an on-chip RX coil. 3.The method of claim 1, wherein the RX coil is approximately equal insize to one resonant coil of the layer of passive, non-overlappingresonant coils.
 4. The method of claim 3, wherein the TX array transferspower to the RX coil with a misalignment factor (MF) of up to 150%,where the MF is a lateral separation of a center of the RX coil from acenter of the excitation coil normalized to a size of the one resonantcoil.
 5. The method of claim 1, wherein an area of the excitation coilis approximately 4 times an area of each resonant coil of the layer ofpassive, non-overlapping resonant coils.
 6. The method of claim 1,wherein the excitation coil and individual resonant coils of theplurality of resonant coils have a substantially square shape.
 7. Themethod of claim 1, wherein the layer of passive, non-overlappingresonant coils is a first layer of passive, non-overlapping resonantcoils and the TX array comprises a second layer of passive,non-overlapping resonant coils located outside the first layer ofpassive, non-overlapping resonant coils opposite the excitation coil,wherein coupling the magnetic field throughout the TX array allows powertransfer to the RX coil when it extends beyond the second layer ofpassive, non-overlapping resonant coils without overlapping the firstlayer of passive, non-overlapping resonant coils.
 8. The method of claim7, wherein individual resonant coils of the first layer and the secondlayer are a uniform size.
 9. The method of claim 8, wherein an area ofthe excitation coil is approximately 4 times an area of each resonantcoil of the layer of passive, non-overlapping resonant coils.
 10. Themethod of claim 7, wherein individual resonant coils of the first layeror the second layer are separated from adjacent resonant coils in thatlayer by a uniform distance.
 11. The method of claim 1, wherein thedevice is a biomedical implant inserted below a skin surface of asubject.
 12. The method of claim 11, comprising positioning the TX arrayon the skin surface adjacent to the RX coil to transfer the power. 13.The method of claim 12, comprising affixing the TX array to the skinsurface.
 14. The method of claim 1, wherein the excitation coil and thelayer of passive, non-overlapping resonant coils are formed on a printedcircuit board (PCB).
 15. The method of claim 14, wherein the excitationcoil and the layer of passive, non-overlapping resonant coils aremulti-turn coils disposed on both sides of the PCB.
 16. The method ofclaim 15, wherein the excitation coil and the plurality of passive,non-overlapping resonant coils comprise two spirally-wound turns on eachside of the PCB.
 17. The method of claim 14, wherein the PCB isflexible.
 18. The method of claim 1, wherein the TX array is formed on aflexible substrate.
 19. The method of claim 1, wherein the TX arraycomprises a plurality of concentric layers of passive, non-overlappingresonant coils surrounding the excitation coil.
 20. The method of claim1, wherein the RF power source excites the excitation coil via an RFpower amplifier.